Limit on Lorentz-Invariance- and CPT-Violating Neutron Spin Interactions Using a ${}^3$He-${}^{129}$Xe Comagnetometer

We performed a search for a Lorentz-invariance- and CPT-violating coupling of the ${}^3$He and ${}^{129}$Xe nuclear spins to posited background fields. Our experimental approach is to measure the free precession of nuclear spin polarized ${}^3$He and ${}^{129}$Xe atoms using SQUID detectors. As the laboratory reference frame rotates with respect to distant stars, we look for a sidereal modulation of the Larmor frequencies of the co-located spin samples. As a result we obtain an upper limit on the equatorial component of the background field ${\tilde{b}}_{\mathrm{\perp }}^n<8.4\cdot {10}^{-34}$ GeV (68% C.L.). Furthermore, this technique was modified to search for an electric dipole moment (EDM) of ${}^{129}$Xe.